An LPP with objective function Z = 4x + 6y is solved by the iso-profit method. The iso-profit lines 4x + 6y = k, for different values of k, are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → parallel lines with slope \(-\displaystyle\frac{2}{3}\)
An iso-profit line joins all the points that give the same profit k. Write 4x + 6y = k in the form y = mx + c:
\(6y = -4x + k\)
\(y = -\displaystyle\frac{2}{3}x + \displaystyle\frac{k}{6}\)
The slope \(-\displaystyle\frac{2}{3}\) does not depend on k; only the intercept changes. So the iso-profit lines are parallel, and a larger k gives a line farther from the origin.
Why the other options are incorrect
Option (2) parallel lines with slope \(-\displaystyle\frac{3}{2}\) — Incorrect. The slope is \(-\displaystyle\frac{4}{6} = -\displaystyle\frac{2}{3}\), not its reciprocal.
Option (3) parallel lines with slope \(\displaystyle\frac{2}{3}\) — Incorrect. The sign is wrong: as x increases, y must decrease to keep 4x + 6y fixed.
Option (4) lines through the origin with different slopes — Incorrect. Only the line with k = 0 passes through the origin, and all the lines have the same slope.